Question

two bodies of masses m1 and m2 have same momentum .Find ratios of kinetic energy

Answer 1

Kinetic Energy of a body in terms of momentum

$= \frac{ {p}^{2} }{2m}$

Therefore the ratio of Kinetic energy

$\frac{K.E.1}{K.E.2} = \frac{ \frac{{p1}^{2}}{2m1}}{ \frac{{p2}^{2}}{2m2}}$

p1 = p2 ( given )

So,

$\frac{K.E.1}{K.E.2} = \frac{ m2 }{m1}$

Above is your answer.

Note:
p1 & m1 is momentum and mass of body 1
p2 & m2 is momentum and mass of body 2

Answer 2

Given: Two bodies of masses m₁ and m₂ have same momentum.

To find: the ratio of their kinetic energy.

Solution: We know from the relationship between kinetic energy and momentum that:

                   K.E. = p²/ 2m ____(1)

Momentum of the masses is equal implying:

              p₁ = p₂ = p _____(2)

From (1), (2) and as per the question:

                  K.E.₁/ K.E.₂ = p²/ 2m₁ × 2m₂/ p²

                  K.E.₁/ K.E.₂ = m₂ / m₁

Hence, the ratio of kinetic energy is m₂ : m₁.